A catalyst for purifying components included in an exhaust gas discharged from a combustion chamber of an internal combustion engine is described in the Patent Literature 1. This catalyst has an active element (that is, an element for activating an oxidation reaction or a reduction reaction of the components included in the exhaust gas) and a composite oxide comprising a composite oxide which carries the active element. Further, this catalyst has a property that the active element transforms into the composite oxide as a solid solution when an atmosphere of the interior of the catalyst is an oxidation atmosphere and the active element precipitates from the composite oxide when the atmosphere of the interior of the catalyst is a reduction atmosphere.